On page 90 of the von Glasersfeld article, he mentions three aphorisms attributed to von Humboldt. Were these based on his observations of people (or did he perform some sort of research to come up with these)? CZ 5/17
Kamii spends some time exploring the differences between Piaget's theory and behaviorism, and claims that his theory explains everything behaviorism can explain, but not vica versa (p. 16). I don't totally agree with this position, and feel Kamii did not support the claim enough. (JE, 5/18)
How does Kamii's use of manipulatives as symbols compare with Wheatley's position that manipulatives are not always a good thing? (JE, 5/18)
social interaction - sociocognitive conflict (Kamii, 2000, p. 44)
re-presentation (von Glasersfeld, 1995)
How are representaiton (re-presentation), abstraction, and reflection related?
- "chilren represent their ideas about reality and not reality itself" (Kamii, 2000, p. 23)
Week 3 (May 26)
I'd like to discuss some the critiques of Piaget (Resnick & Ford, 1981, pp. 174-177), especially in connection to current standardized testing. (JE, 5/25)
Week 4 (June 2)
I would still like to spend more time discussing the relationship between re-flection and abstraction, etc. CZ,5/30
I would add to the aforementioned statement, the following question: How related are enactive, iconic, and symbolic representations (Resnick and Ford, 1981) to the re-presentations described by von Glasersfeld (1995)? (JE, 6/1)
I'd love to talk about the section from Resnick and Ford (1981) with the heading "Questions raised by the structure-oriented approaches." I found many of these questions quite intriguing. (JE, 6/1)
On page 110 (the last full paragraph) Resnick and Ford mention that "one might argue, however, that it is more effective to present the algorithm first and then to introduce the underlying principles once the child is familiar with the steps of the algorithm." In context, does this statement refer to a case that we have discussed in which this process makes sense to us (as mathematicians) but may not make sense to our students? CZ,5/30
After reading the chapter by Silver, I was struck by a question. What position would he take on the following: (1) conceptual knowledge comes before procedural knowledge; (2) procedural knowledge comes before conceptual knowledge; (3) conceptual and procedural knowledge are developed simultaneously. (JE, 6/1)
How are the "structure-oriented" approach by Bruner and ideas in "conceptual/procedural knowledge" related? How similar and how different?
How is the instructional approach using students' cognition such as Bruner's similar or different from the CGI approach?
On page 90 of the von Glasersfeld article, he mentions three aphorisms attributed to von Humboldt. Were these based on his observations of people (or did he perform some sort of research to come up with these)? CZ 5/17
Kamii spends some time exploring the differences between Piaget's theory and behaviorism, and claims that his theory explains everything behaviorism can explain, but not vica versa (p. 16). I don't totally agree with this position, and feel Kamii did not support the claim enough. (JE, 5/18)
How does Kamii's use of manipulatives as symbols compare with Wheatley's position that manipulatives are not always a good thing? (JE, 5/18)
social interaction - sociocognitive conflict (Kamii, 2000, p. 44)
re-presentation (von Glasersfeld, 1995)
How are representaiton (re-presentation), abstraction, and reflection related?
- "chilren represent their ideas about reality and not reality itself" (Kamii, 2000, p. 23)
Week 3 (May 26)
I'd like to discuss some the critiques of Piaget (Resnick & Ford, 1981, pp. 174-177), especially in connection to current standardized testing. (JE, 5/25)
Week 4 (June 2)
I would still like to spend more time discussing the relationship between re-flection and abstraction, etc. CZ,5/30
I would add to the aforementioned statement, the following question: How related are enactive, iconic, and symbolic representations (Resnick and Ford, 1981) to the re-presentations described by von Glasersfeld (1995)? (JE, 6/1)
I'd love to talk about the section from Resnick and Ford (1981) with the heading "Questions raised by the structure-oriented approaches." I found many of these questions quite intriguing. (JE, 6/1)
On page 110 (the last full paragraph) Resnick and Ford mention that "one might argue, however, that it is more effective to present the algorithm first and then to introduce the underlying principles once the child is familiar with the steps of the algorithm." In context, does this statement refer to a case that we have discussed in which this process makes sense to us (as mathematicians) but may not make sense to our students? CZ,5/30
After reading the chapter by Silver, I was struck by a question. What position would he take on the following: (1) conceptual knowledge comes before procedural knowledge; (2) procedural knowledge comes before conceptual knowledge; (3) conceptual and procedural knowledge are developed simultaneously. (JE, 6/1)
How are the "structure-oriented" approach by Bruner and ideas in "conceptual/procedural knowledge" related? How similar and how different?
How is the instructional approach using students' cognition such as Bruner's similar or different from the CGI approach?